Wireless communications services, whatever forms they are in, are provided through radio links, where information such as voice and data is transmitted via modulated electromagnetic waves. Regardless of their forms, all wireless communications systems suffer from adverse propagation effects namely, multipath fading. It is usually caused by the destructive superposition of multipath signals reflected from various types of objects in the propagation environments, creates errors in wireless transmission. One of the common methods used to combat multipath fading is the antenna diversity technique, where two or more antennas at the receiver and/or transmitter are so separated in space or polarization that their fading envelopes are sufficiently decorrelated. A classical combining technique is the maximum-ratio combining (MRC) where the signals from the received antenna elements are weighted such that the signal-to-noise ratio (SNR) of their sum is maximized. However, the MRC technique has so far been used exclusively for receiving applications.
As there are more and more emerging wireless services, many applications require diversity at the transmitter or at both transmitter and receiver. As a result, various transmit diversity techniques have been proposed. For example, a delay transmit diversity scheme was proposed, where the replicas of the signal are transmitted through multiple antennas at different times, thereby minimizing the correlation of the fading envelope at the receiver. Another approach to transmit diversity was to encode the information symbols with forward error correction codes in both space (i.e., antennas displacement) and in time. Another transmit diversity scheme, commonly referred to as space-time block coding (STBC), also makes use of space and time transmission, where a pair of symbols is transmitted using two antennas at first and the transformed version of the pair is transmitted to obtain the MRC-like diversity. However, these transmit diversity techniques are open-loop systems, where it is assumed that there was no information regarding the propagation channel (commonly referred to as “side information”) available at the transmitter.
Side information is, however, available to the transmitter in many systems, such as a time division duplex (TDD) system or a system with feedback. When it is available, side information is proven useful. In fact, closed-loop systems have been proposed to incorporate the side information to improve performance. For example, side information was used in determining the transmission weights for a transmit beamformer to a receiver with a single antenna. Another proposed approach employs the maximum ratio transmission (MRT) technique as a generalization of the maximum ratio algorithm for multiple transmitting antennas and multiple receiving antennas where perfect knowledge of the channel states is assumed. The use of side information was also proposed for carrying out eigen-beamforming at the base transmitter in 3GPP WCDMA. All these schemes assumed the availability of accurate side information of the individual transmission paths or the coefficients of the channel matrix. For a feedback system, this requires a considerable amount of feedback bandwidth. For a system with K transmit antennas and L receive antennas, K×L complex channel coefficients (i.e., 2 K×L scalar values) have to be fed back from the receiver to the transmitter.